Polygon abcd is dilated about the origin, o, to create polygon a′b′c′d′. point a is located at (1, 3), and point a′ is located at (4, 12). which type of dilation was used to create polygon a′b′c′d′, and what is the scale factor? the polygon was enlarged by a scale factor of . the polygon was reduced by a scale factor of . the polygon was enlarged by a scale factor of 4. the polygon was reduced by a scale factor of 4.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

The rectangle shown has a perimeter of 108 cm and the given area. its length is 6 more than five times its width. write and solve a system of equations to find the dimensions of the rectangle.

Afamily has five members. a mom, a dad, two sisters, & a brother. the family lines up single file. what is the probabillity that the mom is at the front of the line